Statistically, you only need about 7 interviews to be pretty confident you'll match in rads. If you get fewer: may you interview well. If you get more, I personally wouldn't start turning down interviews until I was over 10-12 at a minimum. Depends on how much of a gambler you are, how strong your app is relative to the competitiveness of the programs, etc.
From "Charting Outcomes in the Match," 2005 data from the NRMP main residency match, page 56 (google the title to get the pdf file).
Rads Length of match list: number who matched / number who didn't match
1: 7/15 = 32% match rate
2: 10/11 = 48% match rate
3: 15/11 = 58%
4: 17/6 = 74%
5: 14/6 =70%
6: 24/3 = 89%
7: 25/0 = 100%
8: 35/2 =95%
9: 44/0
10: 49/1
11: 52/1
12: 57 /0
13: 58/0
14: 55/0
15: 97/1* *poor guy
> 15: 192/0
A note of explanation: This document has data on the applicant's length of contiguous rank order list. If the med student's rank list goes Rads Program A, Rads Program B, Rads Program C, Internal Med Program A, Int Med B ..., the length of the contiguous rank order list would be 3 for radiology (and 0 for internal medicine).
If we make a few basic assumptions here -- such as, "it's rare for med students to rank a program highly when they haven't gone to an interview at that program" -- then we're saying the length of your contiguous rank list corresponds pretty much to the number of interviews you had.